Research proof index

Proof-ladders A1 reduction statement: the one-time IND-CPA advantage of textbook KEM+DEM is bounded by two KEM IND-CPA advantages plus one DEM IND-CPA advantage, using the canonical left/right and DEM reductions defined above. The runtime coherence hypotheses require runtime.evalDist to be a monad morphism (preserves pure and distributes >>=) and to...

If a KEM and externally keyed DEM are both perfectly correct in the concrete probabilistic semantics of m, then their composition is also perfectly correct.

The T-transform is natural in any oracle-semantics morphism that preserves both the plaintext-to-coins query capability and the distinguished lift of ProbComp.

Completeness theorem for Merkle trees: for any full binary tree with 2 ^ n leaves, and for any index i, the honestly-generated opening proof verifies against the honestly-built root with probability one.

A functional completeness theorem for Merkle proofs built from buildMerkleTree_with_hash.

If f is negligible, then fun n => ↑(p.eval n) * f n is negligible for any polynomial p. This is the key lemma for handling polynomial-loss security reductions.